The long-term motion of comet Halley

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Abstract
The orbital motion of comet Halley has been numerically integrated back to 1404 BC. Beginning with an orbit based upon the 1759, 1682 and 1607 observations of comet Halley, our numerical integration was run back in time with full planetary perturbations and non-gravitational forces taken into account at each 0.5 day time-step. The non-gravitational forces were assumed due to the rocket effect of an outgasing water ice nucleus. Small empirical corrections were made to the computed perihelion passage time in 837 and to the osculating orbital eccentricity in AD 800. In nine cases, the perihelion passage times calculated by Kiang from Chinese observations have been redetermined; we have used the unusually accurate observed perihelion passage times in 837, 374 and 141 to constrain the computed motion of the comet. Osculating orbital elements are given at each apparition from 1910 back to 1404 BC. The dynamic model used to compute the long-term motion of comet Halley successfully represented the ancient Chinese observations over nearly two millennia. This model assumed the comet's non-gravitational forces remained constant from one apparition to the next. Hence it seems likely that comet Halley's spin axis direction and ability to outgas has also remained relatively constant with time over its observed interval. ‘You see therefore an agreement of all the Elements in these three, which would be next to a miracle if they were three different Comets… . Wherefore, if according to what we have already said it should return again about the year 1758, candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.’ E. HALLEY (1752)

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